

A054735


Sum of twin prime pairs.


39



8, 12, 24, 36, 60, 84, 120, 144, 204, 216, 276, 300, 360, 384, 396, 456, 480, 540, 564, 624, 696, 840, 864, 924, 1044, 1140, 1200, 1236, 1284, 1320, 1620, 1644, 1656, 1716, 1764, 2040, 2064, 2100, 2124, 2184, 2304, 2460, 2556, 2580, 2604, 2640, 2856, 2904
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OFFSET

1,1


COMMENTS

(p^q)+(q^p) calculated modulo pq, where (p,q) is the nth twin prime pair. Example: (599^601)+(601^599) == 1200 mod (599*601).  Sam Alexander, Nov 14 2003
El'hakk makes the following claim (without any proof): (q^p)+(p^q) = 2*cosh(q arctanh( sqrt( 1((2/p)^2) ) )) + 2cosh(p arctanh( sqrt( 1((2/q)^2) ) )) mod p*q.  Sam Alexander, Nov 14 2003
Also: Numbers N such that N/21 and N/2+1 both are prime.  M. F. Hasler, Jan 03 2013
Excluding the first term, all remaining terms have digital root 3, 6 or 9.  J. W. Helkenberg, Jul 24 2013
Except for the first term, this sequence is a subsequence of A005101 (Abundant numbers) and of A008594 (Multiples of 12).  Ivan N. Ianakiev, Jul 04 2021


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
El'hakk, Page of the time traveler [Archived copy on web.archive.org, as of Oct 28 2009.]


FORMULA

a(n) = 2*A014574(n) = 4*A040040(n) = A111046(n)/2.
a(n) = 12*A002822(n1) for all n > 1.  M. F. Hasler, Dec 12 2019


EXAMPLE

a(3) = 24 because the twin primes 11 and 13 add to 24.


MAPLE

ZL:=[]:for p from 1 to 1451 do if (isprime(p) and isprime(p+2)) then ZL:=[op(ZL), p+(p+2)]; fi; od; print(ZL); # Zerinvary Lajos, Mar 07 2007
A054735 := proc(n)
2*A001359(n)+2;
end proc: # R. J. Mathar, Jan 06 2013


MATHEMATICA

Select[Table[Prime[n] + 1, {n, 230}], PrimeQ[ # + 1] &] *2 (* Ray Chandler, Oct 12 2005 *)


PROG

(PARI) is_A054735(n)={!bittest(n, 0)&&isprime(n\21)&&isprime(n\2+1)} \\ M. F. Hasler, Jan 03 2013
(PARI) pp=1; forprime(p=1, 1482, if( p==pp+2, print1(p+pp, ", ")); pp=p) \\ Following a suggestion by R. J. Cano, Jan 05 2013
(Haskell)
a054735 = (+ 2) . (* 2) . a001359  Reinhard Zumkeller, Feb 10 2015


CROSSREFS

Cf. A001359, A006512, A014574, A040040, A111046.
Sequence in context: A336583 A333754 A088525 * A162691 A328538 A077566
Adjacent sequences: A054732 A054733 A054734 * A054736 A054737 A054738


KEYWORD

easy,nonn


AUTHOR

Enoch Haga, Apr 22 2000


EXTENSIONS

Additional comments from Ray Chandler, Nov 16 2003
Broken link fixed by M. F. Hasler, Jan 03 2013


STATUS

approved



